Le serrurier arrive afin que nous puissions ouvrir la porte sans casser la serrure.

Because afin que introduces a clause of purpose, and in French that normally requires the subjunctive.

• nous pouvons = indicative
• que nous puissions = subjunctive

So:

• Le serrurier arrive afin que nous puissions ouvrir la porte... = The locksmith is arriving so that we can open the door...

You would not normally say afin que nous pouvons.

Also, puissions is the present subjunctive form of pouvoir for nous.

Afin que means so that or in order that. It expresses purpose.

It is very close in meaning to pour que, but afin que often sounds a bit more formal or written.

• afin que = so that / in order that
• pour que = so that

In everyday speech, many people would naturally say:

• Le serrurier arrive pour que nous puissions ouvrir la porte...

Both are correct here.

Because the fixed expression is afin que when it is followed by a conjugated verb.

Compare:

• afin de + infinitive
• afin que + subjunctive clause

Examples:

• Il vient afin d'aider.
  = He is coming in order to help.

• Il vient afin que nous puissions entrer.
  = He is coming so that we can get in.

In your sentence, the subject after the purpose phrase is nous, so French uses a full clause: afin que nous puissions...

Not naturally in this sentence, because the subject of ouvrir is nous, not le serrurier.

French often uses afin de + infinitive when the subject stays the same:

• Le serrurier arrive afin d'ouvrir la porte. = The locksmith arrives in order to open the door.

That means the locksmith is the one opening the door.

But your sentence says:

• afin que nous puissions ouvrir la porte = so that we can open the door

Since the subject changes, French uses afin que + subjunctive.

Puissions is the present subjunctive form of pouvoir for nous.

Here is the present subjunctive of pouvoir:

• que je puisse
• que tu puisses
• qu'il/elle/on puisse
• que nous puissions
• que vous puissiez
• qu'ils/elles puissent

It looks unusual because pouvoir is irregular.

After sans, French often uses the infinitive when the subject is understood and does not need to be repeated.

• sans casser la serrure = without breaking the lock

This is the most natural phrasing here.

You can use sans que + subjunctive when you want a full clause:

• sans que nous cassions la serrure

That is grammatically possible, but it is heavier and less natural here. French usually prefers the shorter infinitive version in this context.

They are related words, but they mean different things:

• un serrurier = a locksmith
• une serrure = a lock

So in the sentence:

• Le serrurier arrive = The locksmith is arriving
• sans casser la serrure = without breaking the lock

This pair is useful to remember because they look similar.

French often uses the present tense for actions happening now, around now, or in the near future.

• Le serrurier arrive can mean:
  • The locksmith is arriving
  • The locksmith is coming
  • The locksmith arrives

In context, English would usually translate this naturally as is arriving or is coming.

So the French present tense often covers both simple present and present progressive meanings.

Because ouvrir is the infinitive to open, and la porte is its direct object.

French does not need an extra preposition here.

• ouvrir la porte = to open the door
• casser la serrure = to break the lock

This is the normal verb + direct object pattern.

French uses articles more consistently than English.

Here:

• le serrurier = the locksmith
• la porte = the door
• la serrure = the lock

Even when English might sometimes sound more natural with a or no article depending on context, French often still uses the definite article when the thing is specific or understood from the situation.

In this sentence, the locksmith, the door, and the lock are all specific in context.

Not exactly. The verb pouvoir can mean can, to be able to, or sometimes may, depending on context.

Here:

• que nous puissions ouvrir la porte means that we can / may be able to open the door

But in natural English, the best translation is usually:

• so that we can open the door

So yes, there is an idea of possibility or ability, but can is the most natural translation here.

Not with the same meaning.

• Le serrurier arrive pour ouvrir la porte = The locksmith is arriving to open the door

That means the locksmith will open it.

But your sentence says:

• Le serrurier arrive afin que nous puissions ouvrir la porte = The locksmith is arriving so that we can open the door

That suggests his arrival makes it possible for us to open it, perhaps by fixing or unlocking something.

So the grammar change also changes who is doing the opening.

Because sans already means without, so the negative idea is built in.

• sans casser la serrure = without breaking the lock

French does not need an extra negative like ne...pas here.

A careful pronunciation would be approximately:

Luh seh-ru-ryay a-reev ah-fan kuh noo pwee-syohn zoo-vreer lah port sahn kah-say lah seh-rur

A few useful notes:

• serrurier has several sounds English speakers may find tricky.
• puissions is pronounced roughly pwee-syohn.
• In normal speech, nous puissions ouvrir may have a liaison-like flow between words, making it sound connected.
• The final -ent is not pronounced in verb forms like puissent, but here the form is puissions, where the ending is pronounced.

If you want, the sentence can be broken into chunks:

• Le serrurier arrive
• afin que nous puissions
• ouvrir la porte
• sans casser la serrure

That can make it easier to say smoothly.

No, the word order is quite standard for French.

Structure:

• Le serrurier arrive
  main clause

• afin que nous puissions ouvrir la porte
  purpose clause

• sans casser la serrure
  infinitive phrase expressing without doing something

So the overall pattern is:

main action + purpose + manner/result to avoid

This is a very common French sentence structure.